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I understand the problem of reusing the same key in the one-time pad if the cleartext message only contains characters such as A-Z, a-z and spaces.

But what if our cleartext is composed of arbitrary bytes? Which type of attack can we make to find the key or/and decrypt the ciphertext?

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Welcome!

Reusing the same key is fatal to the one-time pad--it does not matter which characters were used in the creation of the truly-random key, from all the possible values on the keyboard, just numbers, just letters, binary, whatever. It can only be used once: that is why they call it the one-time pad.

By definition the one-time pad was generated in a truly random manner. Given such a key that has been properly safeguarded, there is no known attack against it if the one-time pad is properly applied--the key must be at least as long as the plaintext. It is often called the perfect cipher.

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I think you misunderstand the concept of the one-time pad encryption method since the one-time pad treats messages like a binary sequence.

What is done is actually for a message $m$ (this message could be an image, a text, anything, ...), you use its binary representation and XOR its binary value with a binary key $k$ : $m$ $\oplus$ $k$. So it doesn't matter what kind of characters your message contains, you still can't break the security of the scheme when using the same key.

Check out this question: Taking advantage of one-time pad key reuse?

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  • $\begingroup$ You are right that the OTP treats the plaintext as a sequence (encrypts it as a sequence and not a block or blocks), but it does not have to be binary. And the OTP is almost never used for images because that would require an incredibly long truly-random key. And you were right about the characters: it does not matter what kind of characters the OTP contains, as long as it is a real OTP. $\endgroup$ – Patriot Jun 8 '19 at 10:40

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